Hannibal excelled as a tactician. No battle in history is a finer sample of tactics than Cannae. But he was yet greater in logistics and strategy. No captain ever marched to and fro among so many armies of troops superior to his own numbers and material as fearlessly and skillfully as he. No man ever held his own so long or so ably against such odds. Constantly overmatched by better soldiers, led by generals always respectable, often of great ability, he yet defied all their efforts to drive him from Italy, for half a generation. ... As a soldier, in the countenance he presented to the stoutest of foes and in the constancy he exhibited under the bitterest adversity, Hannibal stands alone and unequaled. As a man, no character in history exhibits a purer life or nobler patriotism.

Hannibal's elephants are overrated. He brought them mainly for psychological purposes (namely, to intimidate the various Celtic tribes that inhabited the Alpine regions and encourage them to join his army, which they did). Only one of Hannibal's elephants survived the journey through the Alps, and elephants played almost no role in his victories against the Romans.

In fact, the only major battle where Hannibal deployed elephants against the Romans, at the Battle of Zama in North Africa, was a crushing defeat for the Carthaginians.

Do you have a source confirming African elephants being used by Hannibal, to answer an earlier post?

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Hannibal most likely used the now-extinct North African elephants, which were native to the Atlas Mountains. These elephants were much smaller than either African (i.e. savanna) Elephants or Asian elephants, and it is these elephants that are depicted in most artistic and literary works of the classical Mediterranean.

The interesting story of Ptolemy's elephants comes from another Greek 'historian' Polybius in Raphia (book V) ...

few only of Ptolemy's elephants ventured to close with those of the enemy, and now the men in the towers on the back of these beasts made a gallant fight of it, striking with their pikes at close quarters and wounding each other, while the elephants themselves fought still better, putting forth their whole strength and meeting forehead to forehead. The way in which these animals fight is as follows. With their tusks firmly interlocked they shove with all their might, each trying to force the other to give ground, until the one who proves strongest pushes aside the other's trunk, and then, when he has once made him turn and has him in the flank, he gores him with his tusks as a bull does with his horns. Most of Ptolemy's elephants, however, declined the combat, as is the habit of African elephants; for unable to stand the smell and the trumpeting of the Indian elephants, and terrified, I suppose, also by their great size and strength, they at once turn tail and take to flight before they get near them.

Suggestion:
The slanting posterior of the Indian Elephant differnt distinctly from the humped posterior of the African Elephant. From the pictures and the historical records of Indian Elephants being better in combat than African ones, one could conclude that there is a high possibility that Hannibal's Elephants were Indian indeed.

Sounds more likely to me that Hannibal got his eleghants from Africa because Kerthage did do some serious conquering in Africa before taking on the Romans.

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Let us see what kind of experience the War Elephants would have required.

Hannibal did cross the Alps and invaded Italy from the north and not from the south with elephants. To have elephants negotiate the mountains and survive the weather, you would typically need a breed that is seasoned. Asian elephants fit the bill better than the African ones. The other reason is that African elephants were simply not good enough as war elephants (see post #139).